US6092064A - On-line mining of quantitative association rules - Google Patents

On-line mining of quantitative association rules Download PDF

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Publication number
US6092064A
US6092064A US08/964,064 US96406497A US6092064A US 6092064 A US6092064 A US 6092064A US 96406497 A US96406497 A US 96406497A US 6092064 A US6092064 A US 6092064A
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node
tree
confidence
index
rule
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Charu Chandra Aggarwal
Philip Shi-lung Yu
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International Business Machines Corp
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Priority to US08/964,064 priority Critical patent/US6092064A/en
Priority to TW087112467A priority patent/TW505868B/zh
Priority to PCT/GB1998/002928 priority patent/WO1999023577A1/en
Priority to ES98945396T priority patent/ES2184322T3/es
Priority to JP2000519369A priority patent/JP3575602B2/ja
Priority to CNB988108658A priority patent/CN1138222C/zh
Priority to AU92726/98A priority patent/AU750629B2/en
Priority to KR10-2000-7004749A priority patent/KR100382296B1/ko
Priority to HU0100161A priority patent/HUP0100161A3/hu
Priority to DE69809964T priority patent/DE69809964T2/de
Priority to EP98945396A priority patent/EP1034489B1/en
Priority to PL98340380A priority patent/PL340380A1/xx
Priority to CA002304646A priority patent/CA2304646C/en
Priority to CZ20001630A priority patent/CZ294171B6/cs
Publication of US6092064A publication Critical patent/US6092064A/en
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Priority to HK01104434A priority patent/HK1033987A1/xx
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F16/00—Information retrieval; Database structures therefor; File system structures therefor
    • G06F16/90—Details of database functions independent of the retrieved data types
    • G06F16/95—Retrieval from the web
    • G06F16/951—Indexing; Web crawling techniques
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F16/00—Information retrieval; Database structures therefor; File system structures therefor
    • G06F16/20—Information retrieval; Database structures therefor; File system structures therefor of structured data, e.g. relational data
    • G06F16/22—Indexing; Data structures therefor; Storage structures
    • G06F16/2228—Indexing structures
    • G06F16/2246—Trees, e.g. B+trees
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F16/00—Information retrieval; Database structures therefor; File system structures therefor
    • G06F16/20—Information retrieval; Database structures therefor; File system structures therefor of structured data, e.g. relational data
    • G06F16/24—Querying
    • G06F16/245—Query processing
    • G06F16/2458—Special types of queries, e.g. statistical queries, fuzzy queries or distributed queries
    • G06F16/2465—Query processing support for facilitating data mining operations in structured databases
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F16/00—Information retrieval; Database structures therefor; File system structures therefor
    • G06F16/30—Information retrieval; Database structures therefor; File system structures therefor of unstructured textual data
    • G06F16/31—Indexing; Data structures therefor; Storage structures
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
    • Y10S—TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10S707/00—Data processing: database and file management or data structures
    • Y10S707/953—Organization of data
    • Y10S707/954—Relational
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
    • Y10S—TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10S707/00—Data processing: database and file management or data structures
    • Y10S707/953—Organization of data
    • Y10S707/956—Hierarchical
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
    • Y10S—TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10S707/00—Data processing: database and file management or data structures
    • Y10S707/964—Database arrangement
    • Y10S707/966—Distributed
    • Y10S707/967—Peer-to-peer
    • Y10S707/968—Partitioning
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
    • Y10S—TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10S707/00—Data processing: database and file management or data structures
    • Y10S707/99931—Database or file accessing
    • Y10S707/99932—Access augmentation or optimizing
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
    • Y10S—TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10S707/00—Data processing: database and file management or data structures
    • Y10S707/99931—Database or file accessing
    • Y10S707/99933—Query processing, i.e. searching
    • Y10S707/99936—Pattern matching access

Definitions

  • the present invention relates generally to online searching for data dependencies in large databases and more particularly to an online method of data mining of data items to find quantitative association rules, where the data items comprise various kinds of quantitative and categorical attributes.
  • Data mining also known as knowledge discovery in databases
  • knowledge discovery in databases has been recognized as a new area for database research.
  • the volume of data stored in electronic format has increased dramatically over the past two decades.
  • the increase in use of electronic data gathering devices such as point-of-sale or remote sensing devices has contributed to this explosion of available data.
  • Data storage is becoming easier and more attractive to the business community as the availability of large amounts of computing power and data storage resources are being made available at increasingly reduced costs.
  • Data mining technologies are characterized by intensive computations on large volumes of data.
  • Large databases are definable as consisting of a million records or more.
  • end users will test association rules such as; "75% of customers who buy Cola also buy corn chips", where 75% refers to the rule's confidence factor.
  • the support of the rule is the percentage of transactions that contain both Cola and corn chips.
  • the present invention is directed to a method for efficiently performing online mining of quantitative association rules.
  • An association rule can be generally defined as a conditional statement that suggests that there exists some correlation between its two component parts, antecedent and consequent.
  • both the antecedent and consequent are composed from some user specified combination of quantitative and categorical attributes.
  • the user would provide three additional inputs representing the confidence and support level of interest to the user and a value referred to as interest level. These inputs provide an indication of the strength of the rule proposed by the user (the user query). In other words the strength of the suggested correlation between antecedent and consequent defined by the user query.
  • a method for preprocessing the raw data by utilizing the antecedent attributes to partition the data so as to create a mutidimensional indexing structure,followed by an online rule generation step.
  • pre-processing the data By effectively pre-processing the data into an indexing structure it is placed in a form suitable to answer repeated online queries with practically instantaneous response times.
  • the indexing structure obviates the need to make multiple passes over the database.
  • the indexing structure creates significant performance advantages over previous techniques.
  • the indexing structure (pre-processed data) is stored in such a way that online processing may be done by applying a graph theoretic search algorithm whose complexity is proportional to the size of the output. This results in an online algorithm which is practically instantaneous in terms of response time, minimizing excessive amounts of I/O or computation.
  • FIG. 1 is an overall description of the computer network in which this invention operates.
  • FIG. 2 is an overall description of the method performed by the invention. It consists of two stages described by FIGS. 2(a) and 2(b).
  • FIG. 2(a) is a description of the preprocessing stage.
  • FIG. 2(b) is a description of the on-line stage of the algorithm.
  • FIG. 3 is a detailed description of how the index tree is constructed using the antecedent set. It can be considered an expansion of step 75 of FIG. 2(a).
  • FIG. 4 is a detailed description of how the unmerged rule tree is generated from the index tree. It can be considered an expansion of step 100 of FIG. 2(b).
  • FIG. 5 is a description of how the merged rule tree is built from the unmerged rule tree.
  • FIG. 6 is a description of how the quantitative association rules are generated from the merged rule tree at some user specified interest level r.
  • the present invention is directed to a method for online data mining of quantitative association rules.
  • Traditional database queries consisting of simple questions such as "what were the sales of orange juice in January 1995 for the Long Island area?".
  • Data mining attempts to source out discernible patterns and trends in the data and infers rules from these patterns. With these rules the user is then able to support, review and examine decisions in some related business or scientific area.
  • Typical business decisions associated with the operation concern what to put on sale, how to design coupons, and how to place merchandise on shelves in order to maximize profit, etc. Analysis of past transaction data is a commonly used approach in order to improve the quality of such decisions.
  • An example of an association rule is: 30% of transactions that contain beer also contain diapers; 2% of all transactions contain both of these items". Here 30% is called the confidence of the rule, and 2% the support of the rule.
  • association rule Another example of such an association rule is the statement that 90% of customer transactions that purchase bread and butter also purchase milk.
  • the antecedent of this rule, X consists of bread and butter and the consequent, Y, consists of milk alone.
  • Ninety percent is the confidence factor of the rule. It may be desirable, for instance to find all rules that have "bagels" in the antecedent which may help determine what products (the consequent) may be impacted if the store discontinues selling bagels.
  • the problem of mining association rules is to find all rules that have support and confidence greater than the user-specified minimum support (minsupport s) and minimum confidence (minconfidence c).
  • the rule may be interpreted as:
  • the support and confidence of the rule collectively define the strength of the rule.
  • a non-inclusive yet representative list of the kinds of online queries that such a system can support include;
  • the present method particularizes the method of discovering general association rules to finding quantitative rules from a large database consisting of a set of raw transactions, D, defined by various quantitative and categorical attributes.
  • a typical quantitative/categorical database for a general marketing survey would consist of a series of records where each record reflects some combination of consumer characteristics and preferences;
  • a quantitative association rule is a condition of the form
  • X1, X2, . . . Xk correspond to quantitative antecedent attributes
  • Y1, Y2, . . . Yr, and C correspond to categorical antecedent attributes.
  • [11 . . . u1], [12 . . . u2], . . . [1 k . . . uk] correspond to the ranges for the various quantitative attributes.
  • Z1 and Z2 correspond to a multiple consequent condition.
  • the present method requires that a user supply three inputs, a proposed rule, otherwise referred to as the user query, in the form of an antecedent/consequent pair.
  • a proposed rule otherwise referred to as the user query
  • Minconfidence 50%
  • FIG. 1 is an overall description of the architecture of the present method. There are assumed to be multiple clients 40 which can access the preprocessed data over the network 35.
  • the preprocessed data resides at the server 5. There may be a cache 25 at the server end, along with the preprocessed data 20.
  • the preprocessing as well as the online processing takes place in the CPU 10.
  • a disk 15 is present in the event that the data is stored on disk.
  • the present method comprises two stages, a pre-processing stage followed by an online processing stage.
  • FIG. 2(a) shows an overall description of the preprocessing step as well as the online processing (rule generation steps) for the algorithm.
  • the pre-processing stage involves the construction of a binary index tree structure, see step 75 of FIG. 2 and the associated detailed description of FIG. 3(a).
  • the use of an index tree structure is a well known spatial data structure in the art which is used as a means to index on multidimensional data. Related work in prior art may be found in Guttman, A., A dynamic Index Structure for Spatial Searching. Proceedings of the ACM SIGMOD Conference. In the present method a variation on this index tree structure is employed in order to perform the on-line queries.
  • Antecedent attributes are utilized to partition the data so as to create a multidimensional indexing structure.
  • the indexing structure is a two-level structure where the higher level nodes are associated with at most two successor nodes and lower level nodes may have more than two successor nodes.
  • the construction of the indexing structure is crucial to performing effective online data mining. The key advantage resides in minimizing the amount of disk I/O required to respond to user queries.
  • FIG. 3(b) A graphical analogue of the indexing structure, stored in computer memory, is shown shown in FIG. 3(b) in the form of an index tree.
  • An index tree is a well known spatial data structure which is used in order to index on multi-dimensional data.
  • a separate index structure will be created in computer memory for each dimension, defined by a particular quantitative attribute, specified by the user in the online query.
  • FIG. 3(b) is a specific example of an index tree structure which represents the antecedent condition, "Age" and its associated consequent condition, "FirstTimeBuyer". To further clarify the concept of an index tree, FIG. 3(b) could have represented the "Age" dimension in the example below;
  • the root node of the index tree structure defines the user specified quantitative attribute, Age[0-100].
  • Each of the successive nodes of the tree also represent the quantitative attribute, Age, with increasingly narrower range limits from the top to the bottom of the tree heirarchy.
  • the binary successors to the root node for age[0-100] are Age[0-45] and Age[45-100].
  • the present method stores two pieces of data at each node of the index tree representing the confidence and support levels of interest. For example, with reference to FIG. 3(b), at the root node, two pieces of data are stored consisting of;
  • FIG. 3(a) is the detailed flowchart of the preprocessing stage of the algorithm, illustrated in FIG. 2 as element 100.
  • the process steps of this stage involve generating the binary index tree structure and storing the support and confidence levels for the consequent attribute at each node of the structure, followed by utilizing a compression algorithm on the lower levels of the structure to ensure that the index tree fits into the available memory.
  • Step 300 is the point of entry into the preprocessing stage.
  • Step 310 represents the software to implement the process step of using a binarization algorithm to generate a binary index tree.
  • the binarization step has been discussed in the prior art in Aggarwal C. C., Wolf J., Yu P. S., and Epelman M. A.
  • the S-Tree An efficient index tree for multidimensional index trees.
  • Step 315 the way in which the entries of an index node are organized is unique in that both the support level and the confidence level for each value of the consequent attribute are stored at each node in the structure.
  • Step 320 represents the software to implement the process step of utilizing a compression algorithm to compress the lower level index nodes into a single node.
  • FIG. 4(a) is the detailed flowchart of the primary search algorithm which is used in order to generate the unmerged rule tree from the index tree, illustrated in FIG. 2(b) as element 100.
  • the Querybox is merely a descriptive term to denote the lefthand or antecedent portion of the user query.
  • Example C describes what is required of an online user as input in the present method;
  • An online user would, in addition be required to input a user query (proposed rule) in the form of an an(antecedent/consequent) pair, items 3&4.
  • Item three the Querybox
  • Item four the consequent attribute, can consist of one or more categorical attributes.
  • This user specified query consists of an antecedent condition, querybox, with two dimensions, Age and Lefthandedness, and a single categorical consequent condition, asmoker.
  • This user specified query consists of an antecedent condition, querybox, with two dimensions, Height and Income and a multiple consequent condition.
  • the user specified query consists of a single antecedent condition, querybox, with a single dimension, Age, and a single consequent condition.
  • Example C describes in general terms what a user supplies as input to the method.
  • Example D below provides a representative example. Using the user query in example 2 above, a typical input/output result could look as follows:
  • the output can conceivably generate no rules, one rule, or multiple rules.
  • a single rule was generated in the example above.
  • the generated rule is said to satisfy the user query, (antecedent/consequent pair), at the user specified confidence and support level, 0.5 and 0.4 respectively.
  • Step 400 is the point of entry into the primary search algorithm.
  • Step 410 represents the software to implement the process step of setting a pointer, Currentnode to point to the root node of the index tree. Pointer CurrentNode will always point to the particular node of the index tree which the algorithm is presently searching.
  • Step 420 defines LIST as a set of nodes which are considered to be eligible nodes to be scanned by the search algorithm. LIST is initialized to contain only the root node in step 420.
  • Step 430 represents the software to implement the process step of adding all the child nodes of the node pointed to by Currentnode to LIST which intersect with Querybox Q, and have support at least equal to the user supplied input value, minsupport, s.
  • a child node is said to intersect with Querybox Q, when all of the antecedent conditions associated with the child node are wholly contained within the antecedent condition defined by the Querybox.
  • Step 450 follows steps 440 and 445 and represents the software to implement the process step of deleting the node presently pointed to by Currentnode from LIST and setting the pointer Currentnode to the next node contained in LIST.
  • Step 460 determines whether LIST is empty and terminates the algorithm when the condition is met, see Step 470. Otherwise, the algorithm returns to step 430 and repeats the steps for the node currently pointed to by the pointer CurrentNode.
  • an unmerged rule tree is output which consists of all nodes in the input index tree which satisfy the user specified minimum support, minsupport s.
  • FIG. 5(a) is the detailed flowchart which describes the process of constructing the merged rule tree from the unmerged rule tree.
  • the algorithm described by the flowchart compresses the unmerged rule tree to obtain a hierarchical representation of the rules.
  • the unmerged rule tree is traversed in depth first search order where at each node a determination is made as to whether that node is meaningful.
  • a meaningful node is defined to be a node which has a rule associated with it.
  • a rule may or may not have been associated with a node when the unmerged rule tree was created.
  • FIG. 4(b) the unmerged rule tree, where meaningful nodes correspond to nodes 1, 2, and 4. All meaningful nodes are preserved in the merged rule tree. If a node is determined not to be meaningful then the algorithm either eliminates that node, or merges multiple child nodes into a single node when certain conditions are met.
  • Step 500 represents the point of entry into the algorithm.
  • Step 510 represents the software to implement the process step of insuring that the unmerged rule tree is traversed in depth first search order.
  • Step 515 represents the step of proceeding to the next node in the unmerged rule tree in the depth first traversal.
  • Step 520 represents a decision step which determines whether the current rule node is a meaningful node. A branch is made to step 530 when the current node is determined to be meaningful. Otherwise the algorithm branches to step 540 thereby classifying the node as nonmeaningful.
  • Step 540 is a decision step which determines whether the nonmeaningful node has a child node. If the nonmeaningful node does have a child node a branch is taken to step 550.
  • Step 550 represents the software to implement the process step of deleting the current nonmeaningful node. Otherwise, if it is determined in step 540 that the current node does not have a child node, a branch will be taken to step 560.
  • Step 560 is a decision step for the purpose of determining whether the current nonmeaningful node has one or more than one child nodes. If the current node has only a single child node then a branch is taken to step 570.
  • Step 570 represents the software to implement the process step of deleting the current node and directly connecting the parent and child nodes of the deleted nonmeaningful node together in the index tree. Otherwise, in the case where the current node is found to have multiple child nodes a branch is taken to step 580.
  • Step 580 is a decision step which determines whether the minimum bounding rectangle of the two child nodes are more than that of the nonmeaningful parent node.
  • the minimum bounding rectangle is defined by the upper and lower bounds (the range) of the quantitative attribute for each child node.
  • the ranges of the child nodes are combined and found to be broader than the range of the parent node, a merger occurs. For example, if the child nodes were defined as;
  • Step 590 represents the software to perform the process step of adjusting the minimum bounding rectangle of the parent to be the minimum bounding rectangle of the two child nodes.
  • a branch to decision step 600 determines whether there are any more nodes to traverse in the tree.
  • a branch to termination step 610 occurs if there are no more nodes to traverse, otherwise process steps 490-515 are repeated for the remaining index nodes.
  • FIG. 6 is the detailed flowchart which describes the process of using the merged rule tree as input to define the rules at the user specified interest level r.
  • the merged rule tree is traversed in depth first order.
  • Step 616 is the point of entry into the flowchart.
  • a user would specify an input value for r, representing the interest level.
  • Step 618 represents the software to select the next node in the merged rule tree in depth first order.
  • Step 620 is a decision step which represents the software which looks at all ancestral nodes of the current node of interest to determine whether any of them has a confidence value at least equal to 1/r of the current node.
  • a branch to Step 630 will be taken when condition is true.
  • Step 630 represents the software to prune the rule associated with the current node.
  • Step 640 is a decision step which determines whether there are any remaining nodes to be evaluated in the merged rule tree. The process steps will be repeated if there are additional nodes to be evaluated, otherwise the process terminates at this point.

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Application Number Priority Date Filing Date Title
US08/964,064 US6092064A (en) 1997-11-04 1997-11-04 On-line mining of quantitative association rules
TW087112467A TW505868B (en) 1997-11-04 1998-07-29 On-line mining of quantitative association rules
HU0100161A HUP0100161A3 (en) 1997-11-04 1998-09-29 Online database mining
PL98340380A PL340380A1 (en) 1997-11-04 1998-09-29 Method of acquiring data directly from data base
JP2000519369A JP3575602B2 (ja) 1997-11-04 1998-09-29 ć‚Ŗćƒ³ćƒ©ć‚¤ćƒ³ćƒ»ćƒ‡ćƒ¼ć‚æćƒ™ćƒ¼ć‚¹ćƒ»ćƒžć‚¤ćƒ‹ćƒ³ć‚°
CNB988108658A CN1138222C (zh) 1997-11-04 1998-09-29 åœØēŗæę•°ę®åŗ“ęŒ–ęŽ˜ēš„ę–¹ę³•å’Œč®¾å¤‡
AU92726/98A AU750629B2 (en) 1997-11-04 1998-09-29 Online database mining
KR10-2000-7004749A KR100382296B1 (ko) 1997-11-04 1998-09-29 ģ˜Øė¼ģø ė°ģ“ķ„°ė² ģ“ģŠ¤ ė§ˆģ“ė‹
PCT/GB1998/002928 WO1999023577A1 (en) 1997-11-04 1998-09-29 Online database mining
DE69809964T DE69809964T2 (de) 1997-11-04 1998-09-29 Online-datenbank ausbeutung
EP98945396A EP1034489B1 (en) 1997-11-04 1998-09-29 Online database mining
ES98945396T ES2184322T3 (es) 1997-11-04 1998-09-29 Extraccion de datos en linea.
CA002304646A CA2304646C (en) 1997-11-04 1998-09-29 Online database mining
CZ20001630A CZ294171B6 (cs) 1997-11-04 1998-09-29 ZpÅÆsob pÅ™Ć­mĆ©ho vyhledĆ”vĆ”nĆ­ v rozsĆ”hlĆ© databĆ”zi
HK01104434A HK1033987A1 (en) 1997-11-04 2001-06-27 Method and apparatus for online database mining

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Cited By (48)

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US6185549B1 (en) * 1998-04-29 2001-02-06 Lucent Technologies Inc. Method for mining association rules in data
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